English

The landscape law for tight binding Hamiltonians

Mathematical Physics 2022-09-14 v2 Analysis of PDEs math.MP Spectral Theory

Abstract

The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schr\"odinger operator on Zd\Z^d. In particular, we establish upper and lower bounds for the integrated density of states in terms of the counting function based upon the localization landscape.

Cite

@article{arxiv.2101.03282,
  title  = {The landscape law for tight binding Hamiltonians},
  author = {Douglas N. Arnold and Marcel Filoche and Svitlana Mayboroda and Wei Wang and Shiwen Zhang},
  journal= {arXiv preprint arXiv:2101.03282},
  year   = {2022}
}
R2 v1 2026-06-23T21:56:24.860Z